If caring more for their general health was "caused" by grip strength training than grip strength training is still causative for increasing lifespan.

Think about it. Prescribing grip strength training in this case will indeed increase lifespan if what I said above were true. But the claim people are making here is that the correlation has no causative relation... that prescribing grip strength training WILL NOT cause lifespan to increase.

In fact, everything the article claims is true if the scenario you described is real.

You're thinking about direct causation which is hard to define. If running increases heart health which increases lifespan... which caused lifespan to increase? Heart health or running? The most elegant definition is to say both do. But then again being born is causative to increased lifespan as well but making a statement saying birth causes increased lifespan isn't a meaningful statement.

The nature of causation is a chain of events leading all the way back to the beginning of time. All events in that chain caused the most recent event in the chain. Reality is, in fact, made up of single tree of causative events and multiple linked chains, where ancestors in the tree are said to be causative.

Sibling nodes and events that don't have an ancestor relationship at best can only share a correlation (aka common ancestor).